Related Fractions Lessons

The concepts and methods from the above lesson are also shown below in text and graphic form.

The example below uses a pie, cut into equal pieces, to show equivalent fractions.

Here is half of a pie.

1

2

Here is two fourths of a pie

2

4

Here is four eighths of a pie.

4

8

These are equal fractions of the pie.

So these are equivalent fractions

How to find equivalent fractions

Look at the pie example above. Notice how the top and bottom (numerator and denominator) of the fraction is increasing by a factor of 2. In other words, they are both being multiplied by 2.

Multiplying or dividing both the numerator and denominator of a fraction will result in an equivalent fraction. Here are some more examples:

2

3

Multiply top and bottom by 4

2

3

x 4

x 4

=

8

12

2

3

are equivalent to

8

12

5

6

Multiply top and bottom by 3

5

6

x 3

x 3

=

15

18

5

6

are equivalent to

15

18

8

10

Divide top and bottom by 2

8

10

÷ 2

÷ 2

=

4

5

8

10

are equivalent to

4

5

3

4

Multiply top and bottom by 10

3

4

x 10

x 10

=

30

40

3

4

are equivalent to

30

40

25

100

Divide top and bottom by 25

25

100

÷ 25

÷ 25

=

1

4

25

100

are equivalent to

1

4

Do the same to both the numerator and the denominator

Questions often require equivalent fractions to be written when only the numerator or denominator are given. The examples below show how these questions can be answered.

4

5

=

?

25

What was done to the denominator to get to 25?

It was multiplied by 5

So do the same to the numerator.
4 x 5 = 20

4

5

=

20

25

45

81

=

?

9

What was done to the denominator to get to 9?

It was divided by 9

So do the same to the numerator.
45 ÷ 9 = 5

45

81

=

5

9

3

4

=

18

?

What was done to the numerator to get to 18?

It was multiplied by 6

So do the same to the denominator.
4 x 6 = 24

3

4

=

18

24

Remember: Only use multiplication or division when finding equivalent fractions. Do not use addition or subtraction.

Before moving on to work with fractions it is important that your
child understands equivalency with fractions. Be sure he or she can
accurately determine larger and smaller equivalent fractions. Ask him
or her to describe what they are doing to determine equivalent fractions?

Worksheets

Practice working with equivalent fractions using the worksheets below.